Effect of amorphous surface layers on HRTEM image evaluation

Abstract

The possibility to image atomic columns with high contrast and minimum contrast delocalisation in aberration corrected transmission electron microscopes opened new perspectives to analyse the structural property relationships in crystalline solids. The analysis of composition in strained heterostructures, the structure of ferroelectric domains, or of extended defects are some recent examples. For all these applications the ultimate precision in analysis of atomic positions is required. To measure compositional fluctuations in InGaN quantum wells with a precision of 1% requires a measuring precision of atomic column positionss of 0.5 pm. While the influence of the electron detection system, has attracted attention in the last years and effects like the modulation transfer function and shot noise has been in the focus of some papers, e.g. [1], the effect of amorphous surface layers has attracted less attention. This is the more astonishing since TEM samples are needed to stay in the weak phase object approximation for direct imaging. For such a few nanometer thick samples amorphous surface layers influence the image contrast as they contribute noticeable to the overall phase of the exit wave. We study the influence of amorphous surface layers in detail based on the analysis of image series of thin GaN samples. Amorphous layers are observable as a fluctuating contrast underneath the high‐resolution lattice pattern. The analysis of the unit cell parameters shows that the unit cell parameter in the single image fluctuates by 4.5 pm. In image series we see that the unit cell parameters at a given location fluctuates statistically and gives the impression of ‘jumping’ atomic columns, i.e. a distortion of the unit cell parameter. The STD drops down to 1.5 pm when averaging about all N = 30 images although a reduction to 0.84 pm is expected for random errors ( figure 1). In simulations with shot noise and MTF the highest STD in single images is already smaller than 1 pm. This indicates that the amorphous layers remains the main source for the measurement error. To estimate the origin of the static error in the measurements caused by amorphous layers a systematic analysis was carried out with the aforementioned GaN structure. Using experimental amorphous contrast from the edge of a cross section sample (figure 2) as a model for the noise in image simulation the same reduced improvement in the STD as in the experiment can be observed (figure 1). One could suspect the non vanishing correlation in the amorphous contrast between successive images to be responsible for the static error in the measurement. Therefore uncorrelated patches of amorphous contrast pattern were used in a further image simulation. The result shows again the reduced improvement of the STD, thus we suspected that the source of the static error must lies in the radial distribution function of the amorphous layer. Looking at the frequency distribution in the power spectra of amorphous and crystalline areas it is noticeable that the broader distribution underlying the sharp peaks of the crystalline material is similar to the frequency distribution of the amorphous area. This broad frequency distribution is the result of the nearest neighbour distances in the amorphous network which are in the same range as the inter‐atomic distances in crystalline material. But as the direction of the nearest neighbour bonds are irregular in the amorphous network the projected distances have a broader distribution. Using a random pseudo amorphous network neglecting nearest neighbour distances in a simulated series the STD of the c‐lattice parameter measurement follows the random error rule. By adjusting the amorphous network to inter‐atomic distances a reduced drop in the STD with increasing N is obtained again. In conclusion amorphous surface layers are the limiting factor of relative position measurements in HRTEM lattice patterns on local scale because of the similar nearest neighbour distances in amorphous and in crystalline material which lead to a static measurement error. As a consequence of the similar distances filtering in the frequency domain is not useful to improve local measurements. Instead improvements in the reduction of amorphous surface layers in the sample preparation has to be found. On the other hand measurements of longer distances well above nearest neighbour distances as for example in case of superstructures or ordering phenomena should not be affected by the static error caused by amorphous layers as the correlation is limited to nearest and next nearest neighbour distances.